LMFDB - Embedded newform 2013.2.a.h.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2013,2,Mod(1,2013)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2013, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("2013.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2013 = 3 \cdot 11 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2013.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$16.0738859269$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - x^{13} - 21 x^{12} + 20 x^{11} + 167 x^{10} - 148 x^{9} - 627 x^{8} + 497 x^{7} + 1123 x^{6} + \cdots - 1 $ x^14 - x^13 - 21x^12 + 20x^11 + 167x^10 - 148x^9 - 627x^8 + 497x^7 + 1123x^6 - 745x^5 - 802x^4 + 386x^3 + 74x^2 - 15x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$2.45909$ of defining polynomial
Character	$\chi$	$=$	2013.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.45909 q^{2} -1.00000 q^{3} +4.04715 q^{4} -1.85442 q^{5} +2.45909 q^{6} +2.32343 q^{7} -5.03413 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.45909 q^{2} -1.00000 q^{3} +4.04715 q^{4} -1.85442 q^{5} +2.45909 q^{6} +2.32343 q^{7} -5.03413 q^{8} +1.00000 q^{9} +4.56020 q^{10} -1.00000 q^{11} -4.04715 q^{12} +6.54120 q^{13} -5.71353 q^{14} +1.85442 q^{15} +4.28511 q^{16} +2.94936 q^{17} -2.45909 q^{18} +6.42989 q^{19} -7.50511 q^{20} -2.32343 q^{21} +2.45909 q^{22} -1.80034 q^{23} +5.03413 q^{24} -1.56112 q^{25} -16.0854 q^{26} -1.00000 q^{27} +9.40326 q^{28} +8.87924 q^{29} -4.56020 q^{30} +2.72079 q^{31} -0.469234 q^{32} +1.00000 q^{33} -7.25276 q^{34} -4.30862 q^{35} +4.04715 q^{36} -3.53485 q^{37} -15.8117 q^{38} -6.54120 q^{39} +9.33540 q^{40} -2.27369 q^{41} +5.71353 q^{42} -3.10603 q^{43} -4.04715 q^{44} -1.85442 q^{45} +4.42721 q^{46} +11.7194 q^{47} -4.28511 q^{48} -1.60167 q^{49} +3.83895 q^{50} -2.94936 q^{51} +26.4732 q^{52} +7.91063 q^{53} +2.45909 q^{54} +1.85442 q^{55} -11.6965 q^{56} -6.42989 q^{57} -21.8349 q^{58} -5.84081 q^{59} +7.50511 q^{60} +1.00000 q^{61} -6.69069 q^{62} +2.32343 q^{63} -7.41633 q^{64} -12.1301 q^{65} -2.45909 q^{66} -10.0882 q^{67} +11.9365 q^{68} +1.80034 q^{69} +10.5953 q^{70} +13.7123 q^{71} -5.03413 q^{72} -14.7140 q^{73} +8.69254 q^{74} +1.56112 q^{75} +26.0227 q^{76} -2.32343 q^{77} +16.0854 q^{78} +3.60431 q^{79} -7.94640 q^{80} +1.00000 q^{81} +5.59122 q^{82} -5.22564 q^{83} -9.40326 q^{84} -5.46935 q^{85} +7.63802 q^{86} -8.87924 q^{87} +5.03413 q^{88} -14.1984 q^{89} +4.56020 q^{90} +15.1980 q^{91} -7.28625 q^{92} -2.72079 q^{93} -28.8191 q^{94} -11.9237 q^{95} +0.469234 q^{96} +17.9948 q^{97} +3.93867 q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - q^{2} - 14 q^{3} + 15 q^{4} + q^{5} + q^{6} + 9 q^{7} + 14 q^{9}+O(q^{10}) $ 14 * q - q^2 - 14 * q^3 + 15 * q^4 + q^5 + q^6 + 9 * q^7 + 14 * q^9	\( 14 q - q^{2} - 14 q^{3} + 15 q^{4} + q^{5} + q^{6} + 9 q^{7} + 14 q^{9} + 6 q^{10} - 14 q^{11} - 15 q^{12} + q^{13} - 7 q^{14} - q^{15} + 17 q^{16} - 9 q^{17} - q^{18} + 22 q^{19} + 23 q^{20} - 9 q^{21} + q^{22} + q^{23} + 25 q^{25} + 4 q^{26} - 14 q^{27} + 37 q^{28} - 6 q^{29} - 6 q^{30} + 9 q^{31} + 4 q^{32} + 14 q^{33} + 8 q^{34} + 18 q^{35} + 15 q^{36} + 18 q^{37} + 8 q^{38} - q^{39} + 16 q^{40} - 25 q^{41} + 7 q^{42} + 25 q^{43} - 15 q^{44} + q^{45} + 20 q^{46} + 36 q^{47} - 17 q^{48} + 25 q^{49} + 2 q^{50} + 9 q^{51} - 13 q^{52} + q^{54} - q^{55} - 40 q^{56} - 22 q^{57} + 33 q^{58} + 17 q^{59} - 23 q^{60} + 14 q^{61} - 13 q^{62} + 9 q^{63} - 6 q^{64} - 61 q^{65} - q^{66} + 22 q^{67} + 66 q^{68} - q^{69} + 44 q^{70} - 13 q^{71} + 20 q^{73} - 12 q^{74} - 25 q^{75} + 49 q^{76} - 9 q^{77} - 4 q^{78} + 31 q^{79} + 88 q^{80} + 14 q^{81} + 2 q^{82} + 32 q^{83} - 37 q^{84} + 2 q^{85} - 14 q^{86} + 6 q^{87} - 21 q^{89} + 6 q^{90} + 45 q^{91} - 14 q^{92} - 9 q^{93} - 31 q^{94} + 23 q^{95} - 4 q^{96} + 37 q^{97} - 38 q^{98} - 14 q^{99}+O(q^{100}) \) 14 * q - q^2 - 14 * q^3 + 15 * q^4 + q^5 + q^6 + 9 * q^7 + 14 * q^9 + 6 * q^10 - 14 * q^11 - 15 * q^12 + q^13 - 7 * q^14 - q^15 + 17 * q^16 - 9 * q^17 - q^18 + 22 * q^19 + 23 * q^20 - 9 * q^21 + q^22 + q^23 + 25 * q^25 + 4 * q^26 - 14 * q^27 + 37 * q^28 - 6 * q^29 - 6 * q^30 + 9 * q^31 + 4 * q^32 + 14 * q^33 + 8 * q^34 + 18 * q^35 + 15 * q^36 + 18 * q^37 + 8 * q^38 - q^39 + 16 * q^40 - 25 * q^41 + 7 * q^42 + 25 * q^43 - 15 * q^44 + q^45 + 20 * q^46 + 36 * q^47 - 17 * q^48 + 25 * q^49 + 2 * q^50 + 9 * q^51 - 13 * q^52 + q^54 - q^55 - 40 * q^56 - 22 * q^57 + 33 * q^58 + 17 * q^59 - 23 * q^60 + 14 * q^61 - 13 * q^62 + 9 * q^63 - 6 * q^64 - 61 * q^65 - q^66 + 22 * q^67 + 66 * q^68 - q^69 + 44 * q^70 - 13 * q^71 + 20 * q^73 - 12 * q^74 - 25 * q^75 + 49 * q^76 - 9 * q^77 - 4 * q^78 + 31 * q^79 + 88 * q^80 + 14 * q^81 + 2 * q^82 + 32 * q^83 - 37 * q^84 + 2 * q^85 - 14 * q^86 + 6 * q^87 - 21 * q^89 + 6 * q^90 + 45 * q^91 - 14 * q^92 - 9 * q^93 - 31 * q^94 + 23 * q^95 - 4 * q^96 + 37 * q^97 - 38 * q^98 - 14 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.45909	−1.73884	−0.869421	−	0.494071i	$-0.835508\pi$
$2$	−2.45909	−1.73884	−0.869421	+	0.494071i	$0.835508\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	4.04715	2.02357
$5$	−1.85442	−0.829322	−0.414661	−	0.909976i	$-0.636100\pi$
$5$	−1.85442	−0.829322	−0.414661	+	0.909976i	$0.636100\pi$
$6$	2.45909	1.00392
$7$	2.32343	0.878174	0.439087	−	0.898445i	$-0.355302\pi$
$7$	2.32343	0.878174	0.439087	+	0.898445i	$0.355302\pi$
$8$	−5.03413	−1.77983
$9$	1.00000	0.333333
$10$	4.56020	1.44206
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−4.04715	−1.16831
$13$	6.54120	1.81420	0.907101	−	0.420913i	$-0.138290\pi$
$13$	6.54120	1.81420	0.907101	+	0.420913i	$0.138290\pi$
$14$	−5.71353	−1.52701
$15$	1.85442	0.478809
$16$	4.28511	1.07128
$17$	2.94936	0.715325	0.357663	−	0.933851i	$-0.383574\pi$
$17$	2.94936	0.715325	0.357663	+	0.933851i	$0.383574\pi$
$18$	−2.45909	−0.579614
$19$	6.42989	1.47512	0.737558	−	0.675283i	$-0.235979\pi$
$19$	6.42989	1.47512	0.737558	+	0.675283i	$0.235979\pi$
$20$	−7.50511	−1.67819
$21$	−2.32343	−0.507014
$22$	2.45909	0.524281
$23$	−1.80034	−0.375397	−0.187699	−	0.982227i	$-0.560103\pi$
$23$	−1.80034	−0.375397	−0.187699	+	0.982227i	$0.560103\pi$
$24$	5.03413	1.02759
$25$	−1.56112	−0.312225
$26$	−16.0854	−3.15461
$27$	−1.00000	−0.192450
$28$	9.40326	1.77705
$29$	8.87924	1.64883	0.824417	−	0.565983i	$-0.191503\pi$
$29$	8.87924	1.64883	0.824417	+	0.565983i	$0.191503\pi$
$30$	−4.56020	−0.832574
$31$	2.72079	0.488669	0.244335	−	0.969691i	$-0.421431\pi$
$31$	2.72079	0.488669	0.244335	+	0.969691i	$0.421431\pi$
$32$	−0.469234	−0.0829497
$33$	1.00000	0.174078
$34$	−7.25276	−1.24384
$35$	−4.30862	−0.728289
$36$	4.04715	0.674525
$37$	−3.53485	−0.581126	−0.290563	−	0.956856i	$-0.593843\pi$
$37$	−3.53485	−0.581126	−0.290563	+	0.956856i	$0.593843\pi$
$38$	−15.8117	−2.56500
$39$	−6.54120	−1.04743
$40$	9.33540	1.47606
$41$	−2.27369	−0.355091	−0.177545	−	0.984113i	$-0.556816\pi$
$41$	−2.27369	−0.355091	−0.177545	+	0.984113i	$0.556816\pi$
$42$	5.71353	0.881617
$43$	−3.10603	−0.473665	−0.236832	−	0.971550i	$-0.576109\pi$
$43$	−3.10603	−0.473665	−0.236832	+	0.971550i	$0.576109\pi$
$44$	−4.04715	−0.610131
$45$	−1.85442	−0.276441
$46$	4.42721	0.652757
$47$	11.7194	1.70945	0.854724	−	0.519082i	$-0.173726\pi$
$47$	11.7194	1.70945	0.854724	+	0.519082i	$0.173726\pi$
$48$	−4.28511	−0.618503
$49$	−1.60167	−0.228811
$50$	3.83895	0.542910
$51$	−2.94936	−0.412993
$52$	26.4732	3.67117
$53$	7.91063	1.08661	0.543304	−	0.839536i	$-0.317173\pi$
$53$	7.91063	1.08661	0.543304	+	0.839536i	$0.317173\pi$
$54$	2.45909	0.334640
$55$	1.85442	0.250050
$56$	−11.6965	−1.56300
$57$	−6.42989	−0.851659
$58$	−21.8349	−2.86706
$59$	−5.84081	−0.760409	−0.380204	−	0.924903i	$-0.624146\pi$
$59$	−5.84081	−0.760409	−0.380204	+	0.924903i	$0.624146\pi$
$60$	7.50511	0.968906
$61$	1.00000	0.128037
$61$	1.00000	0.128037
$62$	−6.69069	−0.849719
$63$	2.32343	0.292725
$64$	−7.41633	−0.927042
$65$	−12.1301	−1.50456
$66$	−2.45909	−0.302694
$67$	−10.0882	−1.23246	−0.616232	−	0.787564i	$-0.711342\pi$
$67$	−10.0882	−1.23246	−0.616232	+	0.787564i	$0.711342\pi$
$68$	11.9365	1.44751
$69$	1.80034	0.216736
$70$	10.5953	1.26638
$71$	13.7123	1.62735	0.813676	−	0.581319i	$-0.197463\pi$
$71$	13.7123	1.62735	0.813676	+	0.581319i	$0.197463\pi$
$72$	−5.03413	−0.593278
$73$	−14.7140	−1.72214	−0.861070	−	0.508486i	$-0.830205\pi$
$73$	−14.7140	−1.72214	−0.861070	+	0.508486i	$0.830205\pi$
$74$	8.69254	1.01049
$75$	1.56112	0.180263
$76$	26.0227	2.98501
$77$	−2.32343	−0.264779
$78$	16.0854	1.82132
$79$	3.60431	0.405517	0.202758	−	0.979229i	$-0.435009\pi$
$79$	3.60431	0.405517	0.202758	+	0.979229i	$0.435009\pi$
$80$	−7.94640	−0.888435
$81$	1.00000	0.111111
$82$	5.59122	0.617447
$83$	−5.22564	−0.573589	−0.286794	−	0.957992i	$-0.592590\pi$
$83$	−5.22564	−0.573589	−0.286794	+	0.957992i	$0.592590\pi$
$84$	−9.40326	−1.02598
$85$	−5.46935	−0.593235
$86$	7.63802	0.823629
$87$	−8.87924	−0.951955
$88$	5.03413	0.536640
$89$	−14.1984	−1.50502	−0.752511	−	0.658579i	$-0.771158\pi$
$89$	−14.1984	−1.50502	−0.752511	+	0.658579i	$0.771158\pi$
$90$	4.56020	0.480687
$91$	15.1980	1.59318
$92$	−7.28625	−0.759644
$93$	−2.72079	−0.282133
$94$	−28.8191	−2.97246
$95$	−11.9237	−1.22335
$96$	0.469234	0.0478910
$97$	17.9948	1.82709	0.913547	−	0.406734i	$-0.133332\pi$
$97$	17.9948	1.82709	0.913547	+	0.406734i	$0.133332\pi$
$98$	3.93867	0.397866
$99$	−1.00000	−0.100504
$100$	−6.31810	−0.631810
$101$	−16.6067	−1.65243	−0.826216	−	0.563354i	$-0.809511\pi$
$101$	−16.6067	−1.65243	−0.826216	+	0.563354i	$0.809511\pi$
$102$	7.25276	0.718130
$103$	7.44597	0.733673	0.366836	−	0.930285i	$-0.380441\pi$
$103$	7.44597	0.733673	0.366836	+	0.930285i	$0.380441\pi$
$104$	−32.9292	−3.22898
$105$	4.30862	0.420478
$106$	−19.4530	−1.88944
$107$	12.3092	1.18997	0.594986	−	0.803736i	$-0.297158\pi$
$107$	12.3092	1.18997	0.594986	+	0.803736i	$0.297158\pi$
$108$	−4.04715	−0.389437
$109$	−14.4228	−1.38146	−0.690728	−	0.723115i	$-0.742710\pi$
$109$	−14.4228	−1.38146	−0.690728	+	0.723115i	$0.742710\pi$
$110$	−4.56020	−0.434798
$111$	3.53485	0.335513
$112$	9.95616	0.940768
$113$	−7.36553	−0.692891	−0.346446	−	0.938070i	$-0.612611\pi$
$113$	−7.36553	−0.692891	−0.346446	+	0.938070i	$0.612611\pi$
$114$	15.8117	1.48090
$115$	3.33859	0.311325
$116$	35.9356	3.33654
$117$	6.54120	0.604734
$118$	14.3631	1.32223
$119$	6.85263	0.628180
$120$	−9.33540	−0.852201
$121$	1.00000	0.0909091
$122$	−2.45909	−0.222636
$123$	2.27369	0.205012
$124$	11.0115	0.988858
$125$	12.1671	1.08826
$126$	−5.71353	−0.509002
$127$	10.7526	0.954136	0.477068	−	0.878867i	$-0.341700\pi$
$127$	10.7526	0.954136	0.477068	+	0.878867i	$0.341700\pi$
$128$	19.1759	1.69493
$129$	3.10603	0.273471
$130$	29.8291	2.61619
$131$	−14.8878	−1.30076	−0.650378	−	0.759611i	$-0.725389\pi$
$131$	−14.8878	−1.30076	−0.650378	+	0.759611i	$0.725389\pi$
$132$	4.04715	0.352259
$133$	14.9394	1.29541
$134$	24.8077	2.14306
$135$	1.85442	0.159603
$136$	−14.8475	−1.27316
$137$	−12.2986	−1.05074	−0.525371	−	0.850873i	$-0.676074\pi$
$137$	−12.2986	−1.05074	−0.525371	+	0.850873i	$0.676074\pi$
$138$	−4.42721	−0.376869
$139$	−15.3998	−1.30620	−0.653099	−	0.757273i	$-0.726531\pi$
$139$	−15.3998	−1.30620	−0.653099	+	0.757273i	$0.726531\pi$
$140$	−17.4376	−1.47375
$141$	−11.7194	−0.986951
$142$	−33.7199	−2.82971
$143$	−6.54120	−0.547002
$144$	4.28511	0.357093
$145$	−16.4658	−1.36741
$146$	36.1831	2.99453
$147$	1.60167	0.132104
$148$	−14.3061	−1.17595
$149$	20.3781	1.66944	0.834721	−	0.550673i	$-0.185629\pi$
$149$	20.3781	1.66944	0.834721	+	0.550673i	$0.185629\pi$
$150$	−3.83895	−0.313449
$151$	5.79859	0.471883	0.235941	−	0.971767i	$-0.424183\pi$
$151$	5.79859	0.471883	0.235941	+	0.971767i	$0.424183\pi$
$152$	−32.3689	−2.62546
$153$	2.94936	0.238442
$154$	5.71353	0.460410
$155$	−5.04550	−0.405264
$156$	−26.4732	−2.11955
$157$	12.4274	0.991817	0.495909	−	0.868375i	$-0.334835\pi$
$157$	12.4274	0.991817	0.495909	+	0.868375i	$0.334835\pi$
$158$	−8.86334	−0.705129
$159$	−7.91063	−0.627353
$160$	0.870157	0.0687920
$161$	−4.18297	−0.329664
$162$	−2.45909	−0.193205
$163$	15.7740	1.23551	0.617757	−	0.786369i	$-0.288042\pi$
$163$	15.7740	1.23551	0.617757	+	0.786369i	$0.288042\pi$
$164$	−9.20195	−0.718552
$165$	−1.85442	−0.144366
$166$	12.8503	0.997380
$167$	−11.8094	−0.913840	−0.456920	−	0.889508i	$-0.651047\pi$
$167$	−11.8094	−0.913840	−0.456920	+	0.889508i	$0.651047\pi$
$168$	11.6965	0.902401
$169$	29.7873	2.29133
$170$	13.4497	1.03154
$171$	6.42989	0.491706
$172$	−12.5706	−0.958496
$173$	24.1903	1.83916	0.919578	−	0.392907i	$-0.128531\pi$
$173$	24.1903	1.83916	0.919578	+	0.392907i	$0.128531\pi$
$174$	21.8349	1.65530
$175$	−3.62716	−0.274188
$176$	−4.28511	−0.323002
$177$	5.84081	0.439022
$178$	34.9151	2.61700
$179$	−13.3687	−0.999224	−0.499612	−	0.866249i	$-0.666524\pi$
$179$	−13.3687	−0.999224	−0.499612	+	0.866249i	$0.666524\pi$
$180$	−7.50511	−0.559398
$181$	−18.9666	−1.40977	−0.704887	−	0.709320i	$-0.749002\pi$
$181$	−18.9666	−1.40977	−0.704887	+	0.709320i	$0.749002\pi$
$182$	−37.3734	−2.77030
$183$	−1.00000	−0.0739221
$184$	9.06316	0.668145
$185$	6.55510	0.481941
$186$	6.69069	0.490585
$187$	−2.94936	−0.215679
$188$	47.4301	3.45920
$189$	−2.32343	−0.169005
$190$	29.3215	2.12721
$191$	11.3313	0.819908	0.409954	−	0.912106i	$-0.365545\pi$
$191$	11.3313	0.819908	0.409954	+	0.912106i	$0.365545\pi$
$192$	7.41633	0.535228
$193$	0.588060	0.0423295	0.0211647	−	0.999776i	$-0.493263\pi$
$193$	0.588060	0.0423295	0.0211647	+	0.999776i	$0.493263\pi$
$194$	−44.2509	−3.17703
$195$	12.1301	0.868657
$196$	−6.48221	−0.463015
$197$	26.5822	1.89390	0.946952	−	0.321376i	$-0.104145\pi$
$197$	26.5822	1.89390	0.946952	+	0.321376i	$0.104145\pi$
$198$	2.45909	0.174760
$199$	−4.56330	−0.323484	−0.161742	−	0.986833i	$-0.551711\pi$
$199$	−4.56330	−0.323484	−0.161742	+	0.986833i	$0.551711\pi$
$200$	7.85891	0.555709
$201$	10.0882	0.711564
$202$	40.8375	2.87332
$203$	20.6303	1.44796
$204$	−11.9365	−0.835722
$205$	4.21637	0.294484
$206$	−18.3103	−1.27574
$207$	−1.80034	−0.125132
$208$	28.0298	1.94351
$209$	−6.42989	−0.444764
$210$	−10.5953	−0.731145
$211$	18.2987	1.25973	0.629867	−	0.776703i	$-0.283109\pi$
$211$	18.2987	1.25973	0.629867	+	0.776703i	$0.283109\pi$
$212$	32.0155	2.19883
$213$	−13.7123	−0.939552
$214$	−30.2694	−2.06917
$215$	5.75988	0.392821
$216$	5.03413	0.342529
$217$	6.32157	0.429136
$218$	35.4671	2.40213
$219$	14.7140	0.994278
$220$	7.50511	0.505995
$221$	19.2923	1.29774
$222$	−8.69254	−0.583405
$223$	−4.67679	−0.313181	−0.156590	−	0.987664i	$-0.550050\pi$
$223$	−4.67679	−0.313181	−0.156590	+	0.987664i	$0.550050\pi$
$224$	−1.09023	−0.0728442
$225$	−1.56112	−0.104075
$226$	18.1125	1.20483
$227$	9.63473	0.639480	0.319740	−	0.947505i	$-0.396404\pi$
$227$	9.63473	0.639480	0.319740	+	0.947505i	$0.396404\pi$
$228$	−26.0227	−1.72340
$229$	19.6987	1.30173	0.650863	−	0.759195i	$-0.274407\pi$
$229$	19.6987	1.30173	0.650863	+	0.759195i	$0.274407\pi$
$230$	−8.20991	−0.541345
$231$	2.32343	0.152870
$232$	−44.6993	−2.93465
$233$	9.18049	0.601434	0.300717	−	0.953713i	$-0.402774\pi$
$233$	9.18049	0.601434	0.300717	+	0.953713i	$0.402774\pi$
$234$	−16.0854	−1.05154
$235$	−21.7327	−1.41768
$236$	−23.6386	−1.53874
$237$	−3.60431	−0.234125
$238$	−16.8513	−1.09231
$239$	−7.54022	−0.487736	−0.243868	−	0.969808i	$-0.578416\pi$
$239$	−7.54022	−0.487736	−0.243868	+	0.969808i	$0.578416\pi$
$240$	7.94640	0.512938
$241$	18.7468	1.20759	0.603794	−	0.797141i	$-0.293655\pi$
$241$	18.7468	1.20759	0.603794	+	0.797141i	$0.293655\pi$
$242$	−2.45909	−0.158077
$243$	−1.00000	−0.0641500
$244$	4.04715	0.259092
$245$	2.97018	0.189758
$246$	−5.59122	−0.356483
$247$	42.0592	2.67616
$248$	−13.6968	−0.869750
$249$	5.22564	0.331162
$250$	−29.9200	−1.89231
$251$	−11.1054	−0.700965	−0.350482	−	0.936569i	$-0.613982\pi$
$251$	−11.1054	−0.700965	−0.350482	+	0.936569i	$0.613982\pi$
$252$	9.40326	0.592350
$253$	1.80034	0.113187
$254$	−26.4416	−1.65909
$255$	5.46935	0.342504
$256$	−32.3228	−2.02017
$257$	14.2372	0.888092	0.444046	−	0.896004i	$-0.353543\pi$
$257$	14.2372	0.888092	0.444046	+	0.896004i	$0.353543\pi$
$258$	−7.63802	−0.475522
$259$	−8.21298	−0.510330
$260$	−49.0924	−3.04458
$261$	8.87924	0.549611
$262$	36.6106	2.26181
$263$	23.3083	1.43725	0.718627	−	0.695396i	$-0.244771\pi$
$263$	23.3083	1.43725	0.718627	+	0.695396i	$0.244771\pi$
$264$	−5.03413	−0.309829
$265$	−14.6696	−0.901148
$266$	−36.7374	−2.25251
$267$	14.1984	0.868925
$268$	−40.8283	−2.49398
$269$	−0.631304	−0.0384913	−0.0192456	−	0.999815i	$-0.506126\pi$
$269$	−0.631304	−0.0384913	−0.0192456	+	0.999815i	$0.506126\pi$
$270$	−4.56020	−0.277525
$271$	−12.0422	−0.731510	−0.365755	−	0.930711i	$-0.619189\pi$
$271$	−12.0422	−0.731510	−0.365755	+	0.930711i	$0.619189\pi$
$272$	12.6383	0.766312
$273$	−15.1980	−0.919826
$274$	30.2435	1.82708
$275$	1.56112	0.0941393
$276$	7.28625	0.438581
$277$	4.99666	0.300220	0.150110	−	0.988669i	$-0.452037\pi$
$277$	4.99666	0.300220	0.150110	+	0.988669i	$0.452037\pi$
$278$	37.8697	2.27127
$279$	2.72079	0.162890
$280$	21.6901	1.29623
$281$	−21.8369	−1.30268	−0.651340	−	0.758786i	$-0.725793\pi$
$281$	−21.8369	−1.30268	−0.651340	+	0.758786i	$0.725793\pi$
$282$	28.8191	1.71615
$283$	9.38159	0.557678	0.278839	−	0.960338i	$-0.410050\pi$
$283$	9.38159	0.557678	0.278839	+	0.960338i	$0.410050\pi$
$284$	55.4957	3.29307
$285$	11.9237	0.706300
$286$	16.0854	0.951151
$287$	−5.28276	−0.311831
$288$	−0.469234	−0.0276499
$289$	−8.30127	−0.488310
$290$	40.4911	2.37772
$291$	−17.9948	−1.05487
$292$	−59.5496	−3.48488
$293$	2.56663	0.149944	0.0749720	−	0.997186i	$-0.476113\pi$
$293$	2.56663	0.149944	0.0749720	+	0.997186i	$0.476113\pi$
$294$	−3.93867	−0.229708
$295$	10.8313	0.630624
$296$	17.7949	1.03431
$297$	1.00000	0.0580259
$298$	−50.1118	−2.90290
$299$	−11.7764	−0.681046
$300$	6.31810	0.364776
$301$	−7.21664	−0.415960
$302$	−14.2593	−0.820530
$303$	16.6067	0.954032
$304$	27.5528	1.58026
$305$	−1.85442	−0.106184
$306$	−7.25276	−0.414613
$307$	11.7513	0.670681	0.335341	−	0.942097i	$-0.391149\pi$
$307$	11.7513	0.670681	0.335341	+	0.942097i	$0.391149\pi$
$308$	−9.40326	−0.535801
$309$	−7.44597	−0.423586
$310$	12.4074	0.704690
$311$	0.0431092	0.00244450	0.00122225	−	0.999999i	$-0.499611\pi$
$311$	0.0431092	0.00244450	0.00122225	+	0.999999i	$0.499611\pi$
$312$	32.9292	1.86425
$313$	−9.75221	−0.551227	−0.275614	−	0.961268i	$-0.588881\pi$
$313$	−9.75221	−0.551227	−0.275614	+	0.961268i	$0.588881\pi$
$314$	−30.5602	−1.72461
$315$	−4.30862	−0.242763
$316$	14.5872	0.820593
$317$	−12.6416	−0.710023	−0.355011	−	0.934862i	$-0.615523\pi$
$317$	−12.6416	−0.710023	−0.355011	+	0.934862i	$0.615523\pi$
$318$	19.4530	1.09087
$319$	−8.87924	−0.497142
$320$	13.7530	0.768816
$321$	−12.3092	−0.687031
$322$	10.2863	0.573234
$323$	18.9641	1.05519
$324$	4.04715	0.224842
$325$	−10.2116	−0.566439
$326$	−38.7897	−2.14836
$327$	14.4228	0.797584
$328$	11.4460	0.632002
$329$	27.2292	1.50119
$330$	4.56020	0.251031
$331$	24.4514	1.34397	0.671986	−	0.740564i	$-0.265441\pi$
$331$	24.4514	1.34397	0.671986	+	0.740564i	$0.265441\pi$
$332$	−21.1489	−1.16070
$333$	−3.53485	−0.193709
$334$	29.0405	1.58902
$335$	18.7077	1.02211
$336$	−9.95616	−0.543153
$337$	2.71105	0.147680	0.0738402	−	0.997270i	$-0.476475\pi$
$337$	2.71105	0.147680	0.0738402	+	0.997270i	$0.476475\pi$
$338$	−73.2497	−3.98426
$339$	7.36553	0.400041
$340$	−22.1353	−1.20045
$341$	−2.72079	−0.147339
$342$	−15.8117	−0.854999
$343$	−19.9854	−1.07911
$344$	15.6362	0.843045
$345$	−3.33859	−0.179744
$346$	−59.4863	−3.19800
$347$	−16.5889	−0.890541	−0.445271	−	0.895396i	$-0.646892\pi$
$347$	−16.5889	−0.890541	−0.445271	+	0.895396i	$0.646892\pi$
$348$	−35.9356	−1.92635
$349$	24.3034	1.30093	0.650465	−	0.759536i	$-0.274574\pi$
$349$	24.3034	1.30093	0.650465	+	0.759536i	$0.274574\pi$
$350$	8.91954	0.476769
$351$	−6.54120	−0.349143
$352$	0.469234	0.0250103
$353$	−1.04268	−0.0554963	−0.0277482	−	0.999615i	$-0.508834\pi$
$353$	−1.04268	−0.0554963	−0.0277482	+	0.999615i	$0.508834\pi$
$354$	−14.3631	−0.763390
$355$	−25.4284	−1.34960
$356$	−57.4628	−3.04552
$357$	−6.85263	−0.362680
$358$	32.8749	1.73749
$359$	9.78110	0.516226	0.258113	−	0.966115i	$-0.416899\pi$
$359$	9.78110	0.516226	0.258113	+	0.966115i	$0.416899\pi$
$360$	9.33540	0.492019
$361$	22.3434	1.17597
$362$	46.6406	2.45138
$363$	−1.00000	−0.0524864
$364$	61.5086	3.22393
$365$	27.2859	1.42821
$366$	2.45909	0.128539
$367$	5.48502	0.286316	0.143158	−	0.989700i	$-0.454274\pi$
$367$	5.48502	0.286316	0.143158	+	0.989700i	$0.454274\pi$
$368$	−7.71467	−0.402155
$369$	−2.27369	−0.118364
$370$	−16.1196	−0.838019
$371$	18.3798	0.954231
$372$	−11.0115	−0.570917
$373$	−21.6216	−1.11952	−0.559761	−	0.828654i	$-0.689107\pi$
$373$	−21.6216	−1.11952	−0.559761	+	0.828654i	$0.689107\pi$
$374$	7.25276	0.375031
$375$	−12.1671	−0.628306
$376$	−58.9969	−3.04254
$377$	58.0809	2.99132
$378$	5.71353	0.293872
$379$	29.0189	1.49060	0.745301	−	0.666729i	$-0.232306\pi$
$379$	29.0189	1.49060	0.745301	+	0.666729i	$0.232306\pi$
$380$	−48.2570	−2.47553
$381$	−10.7526	−0.550870
$382$	−27.8649	−1.42569
$383$	−3.92201	−0.200406	−0.100203	−	0.994967i	$-0.531949\pi$
$383$	−3.92201	−0.200406	−0.100203	+	0.994967i	$0.531949\pi$
$384$	−19.1759	−0.978568
$385$	4.30862	0.219587
$386$	−1.44610	−0.0736043
$387$	−3.10603	−0.157888
$388$	72.8276	3.69726
$389$	−25.9769	−1.31708	−0.658541	−	0.752545i	$-0.728826\pi$
$389$	−25.9769	−1.31708	−0.658541	+	0.752545i	$0.728826\pi$
$390$	−29.8291	−1.51046
$391$	−5.30986	−0.268531
$392$	8.06304	0.407245
$393$	14.8878	0.750991
$394$	−65.3681	−3.29320
$395$	−6.68391	−0.336304
$396$	−4.04715	−0.203377
$397$	19.1899	0.963114	0.481557	−	0.876415i	$-0.340071\pi$
$397$	19.1899	0.963114	0.481557	+	0.876415i	$0.340071\pi$
$398$	11.2216	0.562488
$399$	−14.9394	−0.747905
$400$	−6.68959	−0.334480
$401$	9.45087	0.471954	0.235977	−	0.971759i	$-0.424171\pi$
$401$	9.45087	0.471954	0.235977	+	0.971759i	$0.424171\pi$
$402$	−24.8077	−1.23730
$403$	17.7972	0.886544
$404$	−67.2099	−3.34382
$405$	−1.85442	−0.0921469
$406$	−50.7319	−2.51778
$407$	3.53485	0.175216
$408$	14.8475	0.735059
$409$	−25.7554	−1.27352	−0.636762	−	0.771061i	$-0.719727\pi$
$409$	−25.7554	−1.27352	−0.636762	+	0.771061i	$0.719727\pi$
$410$	−10.3685	−0.512062
$411$	12.2986	0.606647
$412$	30.1349	1.48464
$413$	−13.5707	−0.667771
$414$	4.42721	0.217586
$415$	9.69054	0.475690
$416$	−3.06935	−0.150487
$417$	15.3998	0.754134
$418$	15.8117	0.773376
$419$	−7.79219	−0.380674	−0.190337	−	0.981719i	$-0.560958\pi$
$419$	−7.79219	−0.380674	−0.190337	+	0.981719i	$0.560958\pi$
$420$	17.4376	0.850868
$421$	−28.5371	−1.39081	−0.695407	−	0.718616i	$-0.744776\pi$
$421$	−28.5371	−1.39081	−0.695407	+	0.718616i	$0.744776\pi$
$422$	−44.9983	−2.19048
$423$	11.7194	0.569816
$424$	−39.8231	−1.93398
$425$	−4.60432	−0.223342
$426$	33.7199	1.63373
$427$	2.32343	0.112439
$428$	49.8170	2.40800
$429$	6.54120	0.315812
$430$	−14.1641	−0.683054
$431$	−0.647148	−0.0311720	−0.0155860	−	0.999879i	$-0.504961\pi$
$431$	−0.647148	−0.0311720	−0.0155860	+	0.999879i	$0.504961\pi$
$432$	−4.28511	−0.206168
$433$	−18.4583	−0.887052	−0.443526	−	0.896262i	$-0.646273\pi$
$433$	−18.4583	−0.887052	−0.443526	+	0.896262i	$0.646273\pi$
$434$	−15.5453	−0.746201
$435$	16.4658	0.789477
$436$	−58.3713	−2.79548
$437$	−11.5760	−0.553755
$438$	−36.1831	−1.72889
$439$	8.86799	0.423246	0.211623	−	0.977351i	$-0.432125\pi$
$439$	8.86799	0.423246	0.211623	+	0.977351i	$0.432125\pi$
$440$	−9.33540	−0.445048
$441$	−1.60167	−0.0762702
$442$	−47.4417	−2.25657
$443$	11.3375	0.538661	0.269330	−	0.963048i	$-0.413198\pi$
$443$	11.3375	0.538661	0.269330	+	0.963048i	$0.413198\pi$
$444$	14.3061	0.678936
$445$	26.3297	1.24815
$446$	11.5007	0.544572
$447$	−20.3781	−0.963853
$448$	−17.2313	−0.814104
$449$	−17.3627	−0.819397	−0.409698	−	0.912221i	$-0.634366\pi$
$449$	−17.3627	−0.819397	−0.409698	+	0.912221i	$0.634366\pi$
$450$	3.83895	0.180970
$451$	2.27369	0.107064
$452$	−29.8094	−1.40212
$453$	−5.79859	−0.272442
$454$	−23.6927	−1.11195
$455$	−28.1835	−1.32126
$456$	32.3689	1.51581
$457$	−16.9050	−0.790783	−0.395391	−	0.918513i	$-0.629391\pi$
$457$	−16.9050	−0.790783	−0.395391	+	0.918513i	$0.629391\pi$
$458$	−48.4409	−2.26350
$459$	−2.94936	−0.137664
$460$	13.5118	0.629990
$461$	−31.3017	−1.45786	−0.728932	−	0.684586i	$-0.759983\pi$
$461$	−31.3017	−1.45786	−0.728932	+	0.684586i	$0.759983\pi$
$462$	−5.71353	−0.265818
$463$	−21.3893	−0.994044	−0.497022	−	0.867738i	$-0.665573\pi$
$463$	−21.3893	−0.994044	−0.497022	+	0.867738i	$0.665573\pi$
$464$	38.0485	1.76636
$465$	5.04550	0.233979
$466$	−22.5757	−1.04580
$467$	38.0400	1.76028	0.880142	−	0.474711i	$-0.157448\pi$
$467$	38.0400	1.76028	0.880142	+	0.474711i	$0.157448\pi$
$468$	26.4732	1.22372
$469$	−23.4391	−1.08232
$470$	53.4427	2.46513
$471$	−12.4274	−0.572626
$472$	29.4034	1.35340
$473$	3.10603	0.142815
$474$	8.86334	0.407107
$475$	−10.0379	−0.460568
$476$	27.7336	1.27117
$477$	7.91063	0.362203
$478$	18.5421	0.848096
$479$	36.1392	1.65124	0.825621	−	0.564226i	$-0.190825\pi$
$479$	36.1392	1.65124	0.825621	+	0.564226i	$0.190825\pi$
$480$	−0.870157	−0.0397171
$481$	−23.1222	−1.05428
$482$	−46.1001	−2.09980
$483$	4.18297	0.190332
$484$	4.04715	0.183961
$485$	−33.3699	−1.51525
$486$	2.45909	0.111547
$487$	−19.8680	−0.900306	−0.450153	−	0.892951i	$-0.648631\pi$
$487$	−19.8680	−0.900306	−0.450153	+	0.892951i	$0.648631\pi$
$488$	−5.03413	−0.227884
$489$	−15.7740	−0.713324
$490$	−7.30395	−0.329959
$491$	−23.2929	−1.05119	−0.525597	−	0.850733i	$-0.676158\pi$
$491$	−23.2929	−1.05119	−0.525597	+	0.850733i	$0.676158\pi$
$492$	9.20195	0.414856
$493$	26.1881	1.17945
$494$	−103.427	−4.65342
$495$	1.85442	0.0833500
$496$	11.6589	0.523500
$497$	31.8596	1.42910
$498$	−12.8503	−0.575838
$499$	−18.7308	−0.838504	−0.419252	−	0.907870i	$-0.637708\pi$
$499$	−18.7308	−0.838504	−0.419252	+	0.907870i	$0.637708\pi$
$500$	49.2420	2.20217
$501$	11.8094	0.527606
$502$	27.3092	1.21887
$503$	−22.9645	−1.02393	−0.511967	−	0.859005i	$-0.671083\pi$
$503$	−22.9645	−1.02393	−0.511967	+	0.859005i	$0.671083\pi$
$504$	−11.6965	−0.521001
$505$	30.7959	1.37040
$506$	−4.42721	−0.196814
$507$	−29.7873	−1.32290
$508$	43.5172	1.93076
$509$	−16.0499	−0.711398	−0.355699	−	0.934601i	$-0.615757\pi$
$509$	−16.0499	−0.711398	−0.355699	+	0.934601i	$0.615757\pi$
$510$	−13.4497	−0.595561
$511$	−34.1869	−1.51234
$512$	41.1329	1.81784
$513$	−6.42989	−0.283886
$514$	−35.0106	−1.54425
$515$	−13.8080	−0.608451
$516$	12.5706	0.553388
$517$	−11.7194	−0.515418
$518$	20.1965	0.887383
$519$	−24.1903	−1.06184
$520$	61.0647	2.67786
$521$	−31.7652	−1.39166	−0.695829	−	0.718208i	$-0.744963\pi$
$521$	−31.7652	−1.39166	−0.695829	+	0.718208i	$0.744963\pi$
$522$	−21.8349	−0.955688
$523$	21.3136	0.931979	0.465990	−	0.884790i	$-0.345698\pi$
$523$	21.3136	0.931979	0.465990	+	0.884790i	$0.345698\pi$
$524$	−60.2532	−2.63217
$525$	3.62716	0.158302
$526$	−57.3174	−2.49916
$527$	8.02460	0.349557
$528$	4.28511	0.186486
$529$	−19.7588	−0.859077
$530$	36.0740	1.56695
$531$	−5.84081	−0.253470
$532$	60.4619	2.62136
$533$	−14.8726	−0.644206
$534$	−34.9151	−1.51092
$535$	−22.8264	−0.986870
$536$	50.7851	2.19358
$537$	13.3687	0.576902
$538$	1.55244	0.0669302
$539$	1.60167	0.0689890
$540$	7.50511	0.322969
$541$	26.7223	1.14888	0.574440	−	0.818547i	$-0.305220\pi$
$541$	26.7223	1.14888	0.574440	+	0.818547i	$0.305220\pi$
$542$	29.6128	1.27198
$543$	18.9666	0.813933
$544$	−1.38394	−0.0593360
$545$	26.7460	1.14567
$546$	37.3734	1.59943
$547$	−1.28637	−0.0550010	−0.0275005	−	0.999622i	$-0.508755\pi$
$547$	−1.28637	−0.0550010	−0.0275005	+	0.999622i	$0.508755\pi$
$548$	−49.7744	−2.12626
$549$	1.00000	0.0426790
$550$	−3.83895	−0.163694
$551$	57.0925	2.43222
$552$	−9.06316	−0.385754
$553$	8.37436	0.356114
$554$	−12.2873	−0.522036
$555$	−6.55510	−0.278249
$556$	−62.3254	−2.64319
$557$	5.02337	0.212847	0.106424	−	0.994321i	$-0.466060\pi$
$557$	5.02337	0.212847	0.106424	+	0.994321i	$0.466060\pi$
$558$	−6.69069	−0.283240
$559$	−20.3171	−0.859324
$560$	−18.4629	−0.780200
$561$	2.94936	0.124522
$562$	53.6990	2.26516
$563$	27.1450	1.14402	0.572012	−	0.820245i	$-0.306163\pi$
$563$	27.1450	1.14402	0.572012	+	0.820245i	$0.306163\pi$
$564$	−47.4301	−1.99717
$565$	13.6588	0.574630
$566$	−23.0702	−0.969714
$567$	2.32343	0.0975749
$568$	−69.0296	−2.89642
$569$	−16.5905	−0.695511	−0.347756	−	0.937585i	$-0.613056\pi$
$569$	−16.5905	−0.695511	−0.347756	+	0.937585i	$0.613056\pi$
$570$	−29.3215	−1.22814
$571$	−6.50125	−0.272069	−0.136035	−	0.990704i	$-0.543436\pi$
$571$	−6.50125	−0.272069	−0.136035	+	0.990704i	$0.543436\pi$
$572$	−26.4732	−1.10690
$573$	−11.3313	−0.473374
$574$	12.9908	0.542225
$575$	2.81056	0.117208
$576$	−7.41633	−0.309014
$577$	0.0196890	0.000819665 0	0.000409832	−	1.00000i	$-0.499870\pi$
$577$	0.0196890	0.000819665 0	0.000409832		1.00000i	$0.499870\pi$
$578$	20.4136	0.849094
$579$	−0.588060	−0.0244389
$580$	−66.6397	−2.76706
$581$	−12.1414	−0.503711
$582$	44.2509	1.83426
$583$	−7.91063	−0.327625
$584$	74.0721	3.06513
$585$	−12.1301	−0.501519
$586$	−6.31159	−0.260729
$587$	4.04780	0.167070	0.0835352	−	0.996505i	$-0.473379\pi$
$587$	4.04780	0.167070	0.0835352	+	0.996505i	$0.473379\pi$
$588$	6.48221	0.267322
$589$	17.4944	0.720844
$590$	−26.6352	−1.09656
$591$	−26.5822	−1.09345
$592$	−15.1472	−0.622548
$593$	−3.29700	−0.135391	−0.0676957	−	0.997706i	$-0.521565\pi$
$593$	−3.29700	−0.135391	−0.0676957	+	0.997706i	$0.521565\pi$
$594$	−2.45909	−0.100898
$595$	−12.7077	−0.520963
$596$	82.4734	3.37824
$597$	4.56330	0.186763
$598$	28.9593	1.18423
$599$	21.4453	0.876232	0.438116	−	0.898918i	$-0.355646\pi$
$599$	21.4453	0.876232	0.438116	+	0.898918i	$0.355646\pi$
$600$	−7.85891	−0.320839
$601$	−13.2402	−0.540080	−0.270040	−	0.962849i	$-0.587037\pi$
$601$	−13.2402	−0.540080	−0.270040	+	0.962849i	$0.587037\pi$
$602$	17.7464	0.723289
$603$	−10.0882	−0.410821
$604$	23.4678	0.954890
$605$	−1.85442	−0.0753929
$606$	−40.8375	−1.65891
$607$	−34.8370	−1.41399	−0.706995	−	0.707218i	$-0.749950\pi$
$607$	−34.8370	−1.41399	−0.706995	+	0.707218i	$0.749950\pi$
$608$	−3.01712	−0.122360
$609$	−20.6303	−0.835982
$610$	4.56020	0.184637
$611$	76.6588	3.10128
$612$	11.9365	0.482504
$613$	−12.0906	−0.488335	−0.244167	−	0.969733i	$-0.578515\pi$
$613$	−12.0906	−0.488335	−0.244167	+	0.969733i	$0.578515\pi$
$614$	−28.8975	−1.16621
$615$	−4.21637	−0.170021
$616$	11.6965	0.471263
$617$	−25.9928	−1.04643	−0.523215	−	0.852201i	$-0.675267\pi$
$617$	−25.9928	−1.04643	−0.523215	+	0.852201i	$0.675267\pi$
$618$	18.3103	0.736550
$619$	22.1655	0.890908	0.445454	−	0.895305i	$-0.353042\pi$
$619$	22.1655	0.890908	0.445454	+	0.895305i	$0.353042\pi$
$620$	−20.4199	−0.820082
$621$	1.80034	0.0722452
$622$	−0.106010	−0.00425060
$623$	−32.9889	−1.32167
$624$	−28.0298	−1.12209
$625$	−14.7573	−0.590291
$626$	23.9816	0.958498
$627$	6.42989	0.256785
$628$	50.2957	2.00702
$629$	−10.4256	−0.415694
$630$	10.5953	0.422127
$631$	16.8967	0.672649	0.336324	−	0.941746i	$-0.390816\pi$
$631$	16.8967	0.672649	0.336324	+	0.941746i	$0.390816\pi$
$632$	−18.1446	−0.721752
$633$	−18.2987	−0.727308
$634$	31.0869	1.23462
$635$	−19.9398	−0.791286
$636$	−32.0155	−1.26950
$637$	−10.4769	−0.415109
$638$	21.8349	0.864452
$639$	13.7123	0.542450
$640$	−35.5602	−1.40564
$641$	15.5118	0.612680	0.306340	−	0.951922i	$-0.400896\pi$
$641$	15.5118	0.612680	0.306340	+	0.951922i	$0.400896\pi$
$642$	30.2694	1.19464
$643$	28.4440	1.12172	0.560861	−	0.827910i	$-0.310470\pi$
$643$	28.4440	1.12172	0.560861	+	0.827910i	$0.310470\pi$
$644$	−16.9291	−0.667099
$645$	−5.75988	−0.226795
$646$	−46.6344	−1.83481
$647$	10.2252	0.401993	0.200996	−	0.979592i	$-0.435582\pi$
$647$	10.2252	0.401993	0.200996	+	0.979592i	$0.435582\pi$
$648$	−5.03413	−0.197759
$649$	5.84081	0.229272
$650$	25.1114	0.984948
$651$	−6.32157	−0.247762
$652$	63.8396	2.50015
$653$	−17.9727	−0.703325	−0.351663	−	0.936127i	$-0.614384\pi$
$653$	−17.9727	−0.703325	−0.351663	+	0.936127i	$0.614384\pi$
$654$	−35.4671	−1.38687
$655$	27.6083	1.07874
$656$	−9.74301	−0.380401
$657$	−14.7140	−0.574047
$658$	−66.9591	−2.61034
$659$	29.6229	1.15394	0.576972	−	0.816764i	$-0.304234\pi$
$659$	29.6229	1.15394	0.576972	+	0.816764i	$0.304234\pi$
$660$	−7.50511	−0.292136
$661$	−27.7945	−1.08108	−0.540540	−	0.841319i	$-0.681780\pi$
$661$	−27.7945	−1.08108	−0.540540	+	0.841319i	$0.681780\pi$
$662$	−60.1284	−2.33696
$663$	−19.2923	−0.749253
$664$	26.3066	1.02089
$665$	−27.7039	−1.07431
$666$	8.69254	0.336829
$667$	−15.9857	−0.618968
$668$	−47.7945	−1.84922
$669$	4.67679	0.180815
$670$	−46.0040	−1.77729
$671$	−1.00000	−0.0386046
$672$	1.09023	0.0420566
$673$	12.3964	0.477846	0.238923	−	0.971039i	$-0.423206\pi$
$673$	12.3964	0.477846	0.238923	+	0.971039i	$0.423206\pi$
$674$	−6.66674	−0.256793
$675$	1.56112	0.0600877
$676$	120.553	4.63667
$677$	34.3788	1.32128	0.660642	−	0.750701i	$-0.270284\pi$
$677$	34.3788	1.32128	0.660642	+	0.750701i	$0.270284\pi$
$678$	−18.1125	−0.695608
$679$	41.8096	1.60451
$680$	27.5335	1.05586
$681$	−9.63473	−0.369204
$682$	6.69069	0.256200
$683$	38.8947	1.48826	0.744132	−	0.668033i	$-0.232863\pi$
$683$	38.8947	1.48826	0.744132	+	0.668033i	$0.232863\pi$
$684$	26.0227	0.995003
$685$	22.8068	0.871404
$686$	49.1460	1.87640
$687$	−19.6987	−0.751551
$688$	−13.3097	−0.507427
$689$	51.7450	1.97133
$690$	8.20991	0.312546
$691$	16.0503	0.610583	0.305291	−	0.952259i	$-0.401246\pi$
$691$	16.0503	0.610583	0.305291	+	0.952259i	$0.401246\pi$
$692$	97.9018	3.72167
$693$	−2.32343	−0.0882598
$694$	40.7938	1.54851
$695$	28.5578	1.08326
$696$	44.6993	1.69432
$697$	−6.70593	−0.254005
$698$	−59.7643	−2.26211
$699$	−9.18049	−0.347238
$700$	−14.6797	−0.554839
$701$	13.3561	0.504454	0.252227	−	0.967668i	$-0.418837\pi$
$701$	13.3561	0.504454	0.252227	+	0.967668i	$0.418837\pi$
$702$	16.0854	0.607105
$703$	−22.7287	−0.857229
$704$	7.41633	0.279514
$705$	21.7327	0.818500
$706$	2.56405	0.0964994
$707$	−38.5846	−1.45112
$708$	23.6386	0.888394
$709$	3.35828	0.126123	0.0630615	−	0.998010i	$-0.479914\pi$
$709$	3.35828	0.126123	0.0630615	+	0.998010i	$0.479914\pi$
$710$	62.5308	2.34674
$711$	3.60431	0.135172
$712$	71.4764	2.67869
$713$	−4.89836	−0.183445
$714$	16.8513	0.630643
$715$	12.1301	0.453641
$716$	−54.1051	−2.02200
$717$	7.54022	0.281595
$718$	−24.0526	−0.897637
$719$	27.5080	1.02588	0.512938	−	0.858426i	$-0.328557\pi$
$719$	27.5080	1.02588	0.512938	+	0.858426i	$0.328557\pi$
$720$	−7.94640	−0.296145
$721$	17.3002	0.644292
$722$	−54.9446	−2.04483
$723$	−18.7468	−0.697201
$724$	−76.7605	−2.85278
$725$	−13.8616	−0.514807
$726$	2.45909	0.0912656
$727$	0.693006	0.0257022	0.0128511	−	0.999917i	$-0.495909\pi$
$727$	0.693006	0.0257022	0.0128511	+	0.999917i	$0.495909\pi$
$728$	−76.5088	−2.83560
$729$	1.00000	0.0370370
$730$	−67.0986	−2.48343
$731$	−9.16080	−0.338824
$732$	−4.04715	−0.149587
$733$	32.4941	1.20020	0.600098	−	0.799927i	$-0.295128\pi$
$733$	32.4941	1.20020	0.600098	+	0.799927i	$0.295128\pi$
$734$	−13.4882	−0.497858
$735$	−2.97018	−0.109557
$736$	0.844782	0.0311391
$737$	10.0882	0.371602
$738$	5.59122	0.205816
$739$	14.7986	0.544374	0.272187	−	0.962244i	$-0.412253\pi$
$739$	14.7986	0.544374	0.272187	+	0.962244i	$0.412253\pi$
$740$	26.5295	0.975243
$741$	−42.0592	−1.54508
$742$	−45.1976	−1.65926
$743$	−24.8498	−0.911649	−0.455825	−	0.890070i	$-0.650656\pi$
$743$	−24.8498	−0.911649	−0.455825	+	0.890070i	$0.650656\pi$
$744$	13.6968	0.502150
$745$	−37.7896	−1.38451
$746$	53.1695	1.94667
$747$	−5.22564	−0.191196
$748$	−11.9365	−0.436442
$749$	28.5995	1.04500
$750$	29.9200	1.09252
$751$	−8.05201	−0.293822	−0.146911	−	0.989150i	$-0.546933\pi$
$751$	−8.05201	−0.293822	−0.146911	+	0.989150i	$0.546933\pi$
$752$	50.2189	1.83129
$753$	11.1054	0.404702
$754$	−142.826	−5.20143
$755$	−10.7530	−0.391343
$756$	−9.40326	−0.341993
$757$	41.7999	1.51924	0.759622	−	0.650365i	$-0.225384\pi$
$757$	41.7999	1.51924	0.759622	+	0.650365i	$0.225384\pi$
$758$	−71.3602	−2.59192
$759$	−1.80034	−0.0653483
$760$	60.0255	2.17736
$761$	−50.6166	−1.83485	−0.917425	−	0.397909i	$-0.869736\pi$
$761$	−50.6166	−1.83485	−0.917425	+	0.397909i	$0.869736\pi$
$762$	26.4416	0.957877
$763$	−33.5104	−1.21316
$764$	45.8596	1.65914
$765$	−5.46935	−0.197745
$766$	9.64460	0.348474
$767$	−38.2059	−1.37953
$768$	32.3228	1.16635
$769$	40.3462	1.45492	0.727461	−	0.686149i	$-0.240700\pi$
$769$	40.3462	1.45492	0.727461	+	0.686149i	$0.240700\pi$
$770$	−10.5953	−0.381828
$771$	−14.2372	−0.512740
$772$	2.37997	0.0856568
$773$	11.9238	0.428869	0.214434	−	0.976738i	$-0.431209\pi$
$773$	11.9238	0.428869	0.214434	+	0.976738i	$0.431209\pi$
$774$	7.63802	0.274543
$775$	−4.24750	−0.152575
$776$	−90.5881	−3.25192
$777$	8.21298	0.294639
$778$	63.8797	2.29020
$779$	−14.6196	−0.523800
$780$	49.0924	1.75779
$781$	−13.7123	−0.490665
$782$	13.0574	0.466933
$783$	−8.87924	−0.317318
$784$	−6.86336	−0.245120
$785$	−23.0457	−0.822536
$786$	−36.6106	−1.30586
$787$	−48.7632	−1.73822	−0.869111	−	0.494618i	$-0.835308\pi$
$787$	−48.7632	−1.73822	−0.869111	+	0.494618i	$0.835308\pi$
$788$	107.582	3.83245
$789$	−23.3083	−0.829799
$790$	16.4364	0.584779
$791$	−17.1133	−0.608479
$792$	5.03413	0.178880
$793$	6.54120	0.232285
$794$	−47.1898	−1.67470
$795$	14.6696	0.520278
$796$	−18.4684	−0.654594
$797$	−19.5299	−0.691785	−0.345893	−	0.938274i	$-0.612424\pi$
$797$	−19.5299	−0.691785	−0.345893	+	0.938274i	$0.612424\pi$
$798$	36.7374	1.30049
$799$	34.5647	1.22281
$800$	0.732533	0.0258989
$801$	−14.1984	−0.501674
$802$	−23.2406	−0.820654
$803$	14.7140	0.519245
$804$	40.8283	1.43990
$805$	7.75698	0.273398
$806$	−43.7651	−1.54156
$807$	0.631304	0.0222229
$808$	83.6005	2.94106
$809$	−26.1404	−0.919049	−0.459524	−	0.888165i	$-0.651980\pi$
$809$	−26.1404	−0.919049	−0.459524	+	0.888165i	$0.651980\pi$
$810$	4.56020	0.160229
$811$	39.3822	1.38289	0.691447	−	0.722427i	$-0.256973\pi$
$811$	39.3822	1.38289	0.691447	+	0.722427i	$0.256973\pi$
$812$	83.4939	2.93006
$813$	12.0422	0.422337
$814$	−8.69254	−0.304673
$815$	−29.2516	−1.02464
$816$	−12.6383	−0.442430
$817$	−19.9714	−0.698711
$818$	63.3350	2.21446
$819$	15.1980	0.531062
$820$	17.0643	0.595911
$821$	18.4817	0.645016	0.322508	−	0.946567i	$-0.395474\pi$
$821$	18.4817	0.645016	0.322508	+	0.946567i	$0.395474\pi$
$822$	−30.2435	−1.05486
$823$	−3.67700	−0.128172	−0.0640861	−	0.997944i	$-0.520413\pi$
$823$	−3.67700	−0.128172	−0.0640861	+	0.997944i	$0.520413\pi$
$824$	−37.4840	−1.30582
$825$	−1.56112	−0.0543514
$826$	33.3717	1.16115
$827$	−3.52277	−0.122499	−0.0612493	−	0.998123i	$-0.519508\pi$
$827$	−3.52277	−0.122499	−0.0612493	+	0.998123i	$0.519508\pi$
$828$	−7.28625	−0.253215
$829$	36.1379	1.25512	0.627560	−	0.778568i	$-0.284054\pi$
$829$	36.1379	1.25512	0.627560	+	0.778568i	$0.284054\pi$
$830$	−23.8299	−0.827150
$831$	−4.99666	−0.173332
$832$	−48.5117	−1.68184
$833$	−4.72392	−0.163674
$834$	−37.8697	−1.31132
$835$	21.8996	0.757868
$836$	−26.0227	−0.900014
$837$	−2.72079	−0.0940444
$838$	19.1617	0.661931
$839$	40.7462	1.40672	0.703358	−	0.710836i	$-0.251683\pi$
$839$	40.7462	1.40672	0.703358	+	0.710836i	$0.251683\pi$
$840$	−21.6901	−0.748381
$841$	49.8409	1.71865
$842$	70.1755	2.41841
$843$	21.8369	0.752103
$844$	74.0576	2.54917
$845$	−55.2381	−1.90025
$846$	−28.8191	−0.990821
$847$	2.32343	0.0798340
$848$	33.8979	1.16406
$849$	−9.38159	−0.321975
$850$	11.3225	0.388357
$851$	6.36394	0.218153
$852$	−55.4957	−1.90125
$853$	42.9702	1.47127	0.735636	−	0.677377i	$-0.236883\pi$
$853$	42.9702	1.47127	0.735636	+	0.677377i	$0.236883\pi$
$854$	−5.71353	−0.195513
$855$	−11.9237	−0.407782
$856$	−61.9660	−2.11795
$857$	−51.7558	−1.76794	−0.883972	−	0.467540i	$-0.845141\pi$
$857$	−51.7558	−1.76794	−0.883972	+	0.467540i	$0.845141\pi$
$858$	−16.0854	−0.549147
$859$	−6.73686	−0.229859	−0.114929	−	0.993374i	$-0.536664\pi$
$859$	−6.73686	−0.229859	−0.114929	+	0.993374i	$0.536664\pi$
$860$	23.3111	0.794902
$861$	5.28276	0.180036
$862$	1.59140	0.0542033
$863$	24.2044	0.823929	0.411964	−	0.911200i	$-0.364843\pi$
$863$	24.2044	0.823929	0.411964	+	0.911200i	$0.364843\pi$
$864$	0.469234	0.0159637
$865$	−44.8590	−1.52525
$866$	45.3908	1.54244
$867$	8.30127	0.281926
$868$	25.5843	0.868389
$869$	−3.60431	−0.122268
$870$	−40.4911	−1.37278
$871$	−65.9886	−2.23594
$872$	72.6064	2.45876
$873$	17.9948	0.609031
$874$	28.4665	0.962892
$875$	28.2694	0.955679
$876$	59.5496	2.01200
$877$	−6.49029	−0.219162	−0.109581	−	0.993978i	$-0.534951\pi$
$877$	−6.49029	−0.219162	−0.109581	+	0.993978i	$0.534951\pi$
$878$	−21.8072	−0.735958
$879$	−2.56663	−0.0865703
$880$	7.94640	0.267873
$881$	27.3311	0.920807	0.460403	−	0.887710i	$-0.347705\pi$
$881$	27.3311	0.920807	0.460403	+	0.887710i	$0.347705\pi$
$882$	3.93867	0.132622
$883$	26.5968	0.895055	0.447528	−	0.894270i	$-0.352305\pi$
$883$	26.5968	0.895055	0.447528	+	0.894270i	$0.352305\pi$
$884$	78.0790	2.62608
$885$	−10.8313	−0.364091
$886$	−27.8800	−0.936647
$887$	0.875150	0.0293846	0.0146923	−	0.999892i	$-0.495323\pi$
$887$	0.875150	0.0293846	0.0146923	+	0.999892i	$0.495323\pi$
$888$	−17.7949	−0.597158
$889$	24.9828	0.837897
$890$	−64.7473	−2.17033
$891$	−1.00000	−0.0335013
$892$	−18.9277	−0.633745
$893$	75.3543	2.52164
$894$	50.1118	1.67599
$895$	24.7912	0.828678
$896$	44.5539	1.48844
$897$	11.7764	0.393202
$898$	42.6966	1.42480
$899$	24.1586	0.805734
$900$	−6.31810	−0.210603
$901$	23.3313	0.777278
$902$	−5.59122	−0.186167
$903$	7.21664	0.240155
$904$	37.0791	1.23323
$905$	35.1720	1.16916
$906$	14.2593	0.473733
$907$	−41.9567	−1.39315	−0.696575	−	0.717484i	$-0.745294\pi$
$907$	−41.9567	−1.39315	−0.696575	+	0.717484i	$0.745294\pi$
$908$	38.9932	1.29403
$909$	−16.6067	−0.550811
$910$	69.3059	2.29747
$911$	28.2659	0.936493	0.468246	−	0.883598i	$-0.344886\pi$
$911$	28.2659	0.936493	0.468246	+	0.883598i	$0.344886\pi$
$912$	−27.5528	−0.912364
$913$	5.22564	0.172943
$914$	41.5710	1.37505
$915$	1.85442	0.0613053
$916$	79.7235	2.63414
$917$	−34.5908	−1.14229
$918$	7.25276	0.239377
$919$	−19.4057	−0.640136	−0.320068	−	0.947395i	$-0.603706\pi$
$919$	−19.4057	−0.640136	−0.320068	+	0.947395i	$0.603706\pi$
$920$	−16.8069	−0.554107
$921$	−11.7513	−0.387218
$922$	76.9738	2.53500
$923$	89.6949	2.95234
$924$	9.40326	0.309345
$925$	5.51834	0.181442
$926$	52.5982	1.72849
$927$	7.44597	0.244558
$928$	−4.16644	−0.136770
$929$	32.2579	1.05835	0.529174	−	0.848513i	$-0.322502\pi$
$929$	32.2579	1.05835	0.529174	+	0.848513i	$0.322502\pi$
$930$	−12.4074	−0.406853
$931$	−10.2986	−0.337522
$932$	37.1548	1.21705
$933$	−0.0431092	−0.00141133
$934$	−93.5441	−3.06086
$935$	5.46935	0.178867
$936$	−32.9292	−1.07633
$937$	−24.4476	−0.798669	−0.399334	−	0.916805i	$-0.630759\pi$
$937$	−24.4476	−0.798669	−0.399334	+	0.916805i	$0.630759\pi$
$938$	57.6390	1.88198
$939$	9.75221	0.318251
$940$	−87.9554	−2.86879
$941$	−6.11565	−0.199365	−0.0996823	−	0.995019i	$-0.531783\pi$
$941$	−6.11565	−0.199365	−0.0996823	+	0.995019i	$0.531783\pi$
$942$	30.5602	0.995706
$943$	4.09342	0.133300
$944$	−25.0285	−0.814609
$945$	4.30862	0.140159
$946$	−7.63802	−0.248333
$947$	26.7450	0.869094	0.434547	−	0.900649i	$-0.356908\pi$
$947$	26.7450	0.869094	0.434547	+	0.900649i	$0.356908\pi$
$948$	−14.5872	−0.473769
$949$	−96.2470	−3.12431
$950$	24.6840	0.800856
$951$	12.6416	0.409932
$952$	−34.4971	−1.11806
$953$	12.5656	0.407041	0.203520	−	0.979071i	$-0.434762\pi$
$953$	12.5656	0.407041	0.203520	+	0.979071i	$0.434762\pi$
$954$	−19.4530	−0.629813
$955$	−21.0131	−0.679967
$956$	−30.5164	−0.986970
$957$	8.87924	0.287025
$958$	−88.8697	−2.87125
$959$	−28.5750	−0.922735
$960$	−13.7530	−0.443876
$961$	−23.5973	−0.761203
$962$	56.8596	1.83323
$963$	12.3092	0.396657
$964$	75.8711	2.44364
$965$	−1.09051	−0.0351048
$966$	−10.2863	−0.330957
$967$	−3.19458	−0.102731	−0.0513655	−	0.998680i	$-0.516357\pi$
$967$	−3.19458	−0.102731	−0.0513655	+	0.998680i	$0.516357\pi$
$968$	−5.03413	−0.161803
$969$	−18.9641	−0.609213
$970$	82.0598	2.63478
$971$	−29.2651	−0.939161	−0.469581	−	0.882890i	$-0.655595\pi$
$971$	−29.2651	−0.939161	−0.469581	+	0.882890i	$0.655595\pi$
$972$	−4.04715	−0.129812
$973$	−35.7805	−1.14707
$974$	48.8574	1.56549
$975$	10.2116	0.327034
$976$	4.28511	0.137163
$977$	−15.0225	−0.480614	−0.240307	−	0.970697i	$-0.577248\pi$
$977$	−15.0225	−0.480614	−0.240307	+	0.970697i	$0.577248\pi$
$978$	38.7897	1.24036
$979$	14.1984	0.453781
$980$	12.0208	0.383989
$981$	−14.4228	−0.460485
$982$	57.2795	1.82786
$983$	−0.886011	−0.0282594	−0.0141297	−	0.999900i	$-0.504498\pi$
$983$	−0.886011	−0.0282594	−0.0141297	+	0.999900i	$0.504498\pi$
$984$	−11.4460	−0.364887
$985$	−49.2946	−1.57066
$986$	−64.3990	−2.05088
$987$	−27.2292	−0.866714
$988$	170.220	5.41541
$989$	5.59191	0.177812
$990$	−4.56020	−0.144933
$991$	19.8350	0.630079	0.315040	−	0.949079i	$-0.397982\pi$
$991$	19.8350	0.630079	0.315040	+	0.949079i	$0.397982\pi$
$992$	−1.27669	−0.0405349
$993$	−24.4514	−0.775943
$994$	−78.3457	−2.48498
$995$	8.46228	0.268272
$996$	21.1489	0.670130
$997$	−17.9119	−0.567275	−0.283638	−	0.958932i	$-0.591541\pi$
$997$	−17.9119	−0.567275	−0.283638	+	0.958932i	$0.591541\pi$
$998$	46.0607	1.45803
$999$	3.53485	0.111838

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2013.2.a.h.1.2	✓	14
3.2	odd	2		6039.2.a.j.1.13		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2013.2.a.h.1.2	✓	14	1.1	even	1	trivial
6039.2.a.j.1.13		14	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 2013 = 3 \cdot 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2013.a (trivial)

\(f(q)\)	\(=\)	\(q-2.45909 q^{2} -1.00000 q^{3} +4.04715 q^{4} -1.85442 q^{5} +2.45909 q^{6} +2.32343 q^{7} -5.03413 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.45909 q^{2} -1.00000 q^{3} +4.04715 q^{4} -1.85442 q^{5} +2.45909 q^{6} +2.32343 q^{7} -5.03413 q^{8} +1.00000 q^{9} +4.56020 q^{10} -1.00000 q^{11} -4.04715 q^{12} +6.54120 q^{13} -5.71353 q^{14} +1.85442 q^{15} +4.28511 q^{16} +2.94936 q^{17} -2.45909 q^{18} +6.42989 q^{19} -7.50511 q^{20} -2.32343 q^{21} +2.45909 q^{22} -1.80034 q^{23} +5.03413 q^{24} -1.56112 q^{25} -16.0854 q^{26} -1.00000 q^{27} +9.40326 q^{28} +8.87924 q^{29} -4.56020 q^{30} +2.72079 q^{31} -0.469234 q^{32} +1.00000 q^{33} -7.25276 q^{34} -4.30862 q^{35} +4.04715 q^{36} -3.53485 q^{37} -15.8117 q^{38} -6.54120 q^{39} +9.33540 q^{40} -2.27369 q^{41} +5.71353 q^{42} -3.10603 q^{43} -4.04715 q^{44} -1.85442 q^{45} +4.42721 q^{46} +11.7194 q^{47} -4.28511 q^{48} -1.60167 q^{49} +3.83895 q^{50} -2.94936 q^{51} +26.4732 q^{52} +7.91063 q^{53} +2.45909 q^{54} +1.85442 q^{55} -11.6965 q^{56} -6.42989 q^{57} -21.8349 q^{58} -5.84081 q^{59} +7.50511 q^{60} +1.00000 q^{61} -6.69069 q^{62} +2.32343 q^{63} -7.41633 q^{64} -12.1301 q^{65} -2.45909 q^{66} -10.0882 q^{67} +11.9365 q^{68} +1.80034 q^{69} +10.5953 q^{70} +13.7123 q^{71} -5.03413 q^{72} -14.7140 q^{73} +8.69254 q^{74} +1.56112 q^{75} +26.0227 q^{76} -2.32343 q^{77} +16.0854 q^{78} +3.60431 q^{79} -7.94640 q^{80} +1.00000 q^{81} +5.59122 q^{82} -5.22564 q^{83} -9.40326 q^{84} -5.46935 q^{85} +7.63802 q^{86} -8.87924 q^{87} +5.03413 q^{88} -14.1984 q^{89} +4.56020 q^{90} +15.1980 q^{91} -7.28625 q^{92} -2.72079 q^{93} -28.8191 q^{94} -11.9237 q^{95} +0.469234 q^{96} +17.9948 q^{97} +3.93867 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - q^{2} - 14 q^{3} + 15 q^{4} + q^{5} + q^{6} + 9 q^{7} + 14 q^{9}+O(q^{10}) \) 14 * q - q^2 - 14 * q^3 + 15 * q^4 + q^5 + q^6 + 9 * q^7 + 14 * q^9	\( 14 q - q^{2} - 14 q^{3} + 15 q^{4} + q^{5} + q^{6} + 9 q^{7} + 14 q^{9} + 6 q^{10} - 14 q^{11} - 15 q^{12} + q^{13} - 7 q^{14} - q^{15} + 17 q^{16} - 9 q^{17} - q^{18} + 22 q^{19} + 23 q^{20} - 9 q^{21} + q^{22} + q^{23} + 25 q^{25} + 4 q^{26} - 14 q^{27} + 37 q^{28} - 6 q^{29} - 6 q^{30} + 9 q^{31} + 4 q^{32} + 14 q^{33} + 8 q^{34} + 18 q^{35} + 15 q^{36} + 18 q^{37} + 8 q^{38} - q^{39} + 16 q^{40} - 25 q^{41} + 7 q^{42} + 25 q^{43} - 15 q^{44} + q^{45} + 20 q^{46} + 36 q^{47} - 17 q^{48} + 25 q^{49} + 2 q^{50} + 9 q^{51} - 13 q^{52} + q^{54} - q^{55} - 40 q^{56} - 22 q^{57} + 33 q^{58} + 17 q^{59} - 23 q^{60} + 14 q^{61} - 13 q^{62} + 9 q^{63} - 6 q^{64} - 61 q^{65} - q^{66} + 22 q^{67} + 66 q^{68} - q^{69} + 44 q^{70} - 13 q^{71} + 20 q^{73} - 12 q^{74} - 25 q^{75} + 49 q^{76} - 9 q^{77} - 4 q^{78} + 31 q^{79} + 88 q^{80} + 14 q^{81} + 2 q^{82} + 32 q^{83} - 37 q^{84} + 2 q^{85} - 14 q^{86} + 6 q^{87} - 21 q^{89} + 6 q^{90} + 45 q^{91} - 14 q^{92} - 9 q^{93} - 31 q^{94} + 23 q^{95} - 4 q^{96} + 37 q^{97} - 38 q^{98} - 14 q^{99}+O(q^{100}) \) 14 * q - q^2 - 14 * q^3 + 15 * q^4 + q^5 + q^6 + 9 * q^7 + 14 * q^9 + 6 * q^10 - 14 * q^11 - 15 * q^12 + q^13 - 7 * q^14 - q^15 + 17 * q^16 - 9 * q^17 - q^18 + 22 * q^19 + 23 * q^20 - 9 * q^21 + q^22 + q^23 + 25 * q^25 + 4 * q^26 - 14 * q^27 + 37 * q^28 - 6 * q^29 - 6 * q^30 + 9 * q^31 + 4 * q^32 + 14 * q^33 + 8 * q^34 + 18 * q^35 + 15 * q^36 + 18 * q^37 + 8 * q^38 - q^39 + 16 * q^40 - 25 * q^41 + 7 * q^42 + 25 * q^43 - 15 * q^44 + q^45 + 20 * q^46 + 36 * q^47 - 17 * q^48 + 25 * q^49 + 2 * q^50 + 9 * q^51 - 13 * q^52 + q^54 - q^55 - 40 * q^56 - 22 * q^57 + 33 * q^58 + 17 * q^59 - 23 * q^60 + 14 * q^61 - 13 * q^62 + 9 * q^63 - 6 * q^64 - 61 * q^65 - q^66 + 22 * q^67 + 66 * q^68 - q^69 + 44 * q^70 - 13 * q^71 + 20 * q^73 - 12 * q^74 - 25 * q^75 + 49 * q^76 - 9 * q^77 - 4 * q^78 + 31 * q^79 + 88 * q^80 + 14 * q^81 + 2 * q^82 + 32 * q^83 - 37 * q^84 + 2 * q^85 - 14 * q^86 + 6 * q^87 - 21 * q^89 + 6 * q^90 + 45 * q^91 - 14 * q^92 - 9 * q^93 - 31 * q^94 + 23 * q^95 - 4 * q^96 + 37 * q^97 - 38 * q^98 - 14 * q^99

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